Slide16.JPG

Slide17.JPG
Slide18.JPG

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

Transcript

Ex 6.1, 15 The total cost C(๐‘ฅ) in Rupees associated with the production of ๐‘ฅ units of an item is given by ๐ถ(๐‘ฅ) = 0.007๐‘ฅ^3 โ€“ 0.003๐‘ฅ2 + 15๐‘ฅ + 4000. Find the marginal cost when 17 units are produced.Since Marginal Cost is Rate of change in Total Cost w.r.t No of units produced Let MC be marginal cost So, MC = ๐’…๐‘ช/๐’…๐’™ Given, Total Cost = C(๐‘ฅ) =0.007๐‘ฅ^3โˆ’0.003๐‘ฅ^2+15๐‘ฅ+4000" " We need to find marginal Cost when 17 units are produced i.e. MC when ๐‘ฅ = 17 MC = ๐‘‘(๐ถ(๐‘ฅ))/๐‘‘๐‘ฅ MC = ๐‘‘(0.007๐‘ฅ^3 โˆ’ 0.003๐‘ฅ^2 + 15๐‘ฅ + 4000)/๐‘‘๐‘ฅ MC = ๐‘‘(0.007๐‘ฅ^3 )/๐‘‘๐‘ฅ โˆ’ ๐‘‘(0.003๐‘ฅ^2 )/๐‘‘๐‘ฅ+ ๐‘‘(15๐‘ฅ)/๐‘‘๐‘ฅ+ ๐‘‘(4000)/๐‘‘๐‘ฅ MC = 0.007 ๐‘‘(๐‘ฅ^3 )/๐‘‘๐‘ฅ โˆ’0.003 ๐‘‘(๐‘ฅ^2 )/๐‘‘๐‘ฅ + 15๐‘‘(๐‘ฅ)/๐‘‘๐‘ฅ+0 MC = 0.007 ร— 3๐‘ฅ^2โˆ’0.003 ร—2๐‘ฅ+15 MC = 0.021๐‘ฅ^2โˆ’0.006๐‘ฅ+15 We need to find MC when ๐‘ฅ=17 Putting ๐’™=๐Ÿ๐Ÿ• MC = 0.021(17)^2โˆ’0.006(17)+15 MC = 6.069 โ€“ 0.102 + 15 MC = 20.967 Hence, the Required Marginal cost is Rs. 20.967

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.